A fuzzy epidemic model based on gradual rules and extension principle

The authors applied the Extension Principle in order to build the consequents of the rules of a fuzzy epidemic model. The main idea is to use a function of a classical model an epidemic system, and with the extension principle to find a fuzzy function which operates on the fuzzy epidemic sets. In this sense, the modelling become less dependent on the experts´ opinions, which is an advantage. Our fuzzy rules are so called gradual rules and the method described above was originally proposed by D. Dubois et al.(1995). In order to validate the proposed method, we applied it to another situation, similar to a SIS (Susceptible-Infected-Susceptible) model, which occurs when the infection is 100% lethal. In this model the individuals are classified in seropositives (when they present antibodies against the infection, which results in protection) and seronegatives (when they do not present these antibodies, so they are considered susceptible to infection). When the disease presents no-subclinical infection, vaccination is the unique way to induce the production of antibodies in non-diseased and live individuals. The seropositive individuals are assumed to lose the immunization status after some time, becoming susceptible again. We produced two MISO models using different inference methods. The results were compared with the experimental data set and with another MISO Model, which is entirely based on expert knowledge and presented in a previous work. The use of the extension principle in the sense of building consequent fuzzy sets of fuzzy rules seems to be an adequate tool to model epidemic problems more complex than treated in this work, since this kind of approach seems to be well modelled by gradual fuzzy rules